Set Theory
Venn Diagram
A Venn diagram usually is a drawing, in which circular areas represent groups of items sharing common properties. The drawing consists of two or more circles, each representing a specific group or set. This process of visualizing logical relationships was devised by John Venn (1834-1923).
Each Venn diagram begins with a rectangle representing the universal set. Then each set of values in the problem is represented by a circle. Any values that belong to more than one set will be placed in the sections where the circles overlap.
The universal set is often the "type" of values that are solutions to the problem. For example, the universal set could be the set of all integers from -10 to +10, set A the set of positive integers in that universe, set B the set of integers divisible by 5 in that universe, and set C the set of elements -1, - 5, and 6.
Universal Set
The Venn diagram at the left shows two sets A and B that overlap. The universal set is U.
Values that belong to both set A and set B are located in the center region labeled where the circles overlap.
Intersection
This region is called the "intersection" of the two sets.(Intersection, is only where the two sets intersect, or overlap.)
Union
The notation represents the entire region covered by both sets A and B (and the section where they overlap). This region is called the "union" of the two sets.(Union, like marriage, brings all of both sets together.) If we cut out sets A and B from the picture above, the remaining region in U, the universal set, is labeled , and is called the complement of the union of sets A and B.
A complement of a set is all of the elements (in the universe) that are NOT in the set.
NOTE*: The complement of a set can be represented with several differing notations.
The complement of set A can be
A Venn diagram usually is a drawing, in which circular areas represent groups of items sharing common properties. The drawing consists of two or more circles, each representing a specific group or set. This process of visualizing logical relationships was devised by John Venn (1834-1923).
Each Venn diagram begins with a rectangle representing the universal set. Then each set of values in the problem is represented by a circle. Any values that belong to more than one set will be placed in the sections where the circles overlap.
The universal set is often the "type" of values that are solutions to the problem. For example, the universal set could be the set of all integers from -10 to +10, set A the set of positive integers in that universe, set B the set of integers divisible by 5 in that universe, and set C the set of elements -1, - 5, and 6.
Universal Set
The Venn diagram at the left shows two sets A and B that overlap. The universal set is U.
Values that belong to both set A and set B are located in the center region labeled where the circles overlap.
Intersection
This region is called the "intersection" of the two sets.(Intersection, is only where the two sets intersect, or overlap.)
Union
The notation represents the entire region covered by both sets A and B (and the section where they overlap). This region is called the "union" of the two sets.(Union, like marriage, brings all of both sets together.) If we cut out sets A and B from the picture above, the remaining region in U, the universal set, is labeled , and is called the complement of the union of sets A and B.
A complement of a set is all of the elements (in the universe) that are NOT in the set.
NOTE*: The complement of a set can be represented with several differing notations.
The complement of set A can be